Coltrane changes

In jazz harmony, the Coltrane changes (Coltrane Matrix or cycle, also known as chromatic third relations and multi-tonic changes) are a harmonic progression variation using substitute chords over common jazz chord progressions. These substitution patterns were first demonstrated by jazz musician John Coltrane on the albums Bags & Trane (on the track "Three Little Words") and Cannonball Adderley Quintet in Chicago (on "Limehouse Blues"). Coltrane continued his explorations on the 1960 album Giant Steps, and expanded upon the substitution cycle in his compositions "Giant Steps" and "Countdown", the latter of which is a reharmonized version of Eddie Vinson's "Tune Up". The Coltrane changes are a standard advanced harmonic substitution used in jazz improvisation.

The changes serve as a pattern of chord substitutions for the ii–V–I progression (supertonic–dominant–tonic)  Play  and are noted for the tonally unusual root movement by major thirds (either up or down by a major third interval as opposed to more typical minor or major second intervals, see steps and skips, thus "Giant Steps"), creating an augmented triad.

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